平稳过程假设检验的一个准则
A criterion for hypothesis testing for stationary processes
摘要：
给定一个有限值样本$X_1,...,X_n$，我们希望测试它是由属于$H_0$族的平稳遍历过程生成的，还是由$H_0$族外的平稳遍历过程生成的。我们要求测试的第一类错误是一致有界的，而第二类错误必须不超过概率为1的有限次数。对于这个概念的一致性，我们提供了家庭$H_0$的存在一个相合检验的充要条件。这个标准说明了应用程序测试的成员参数家庭，推广了一些现有的结果。此外，我们分析了一个更强的概念的一致性，这需要有限样本保证的错误的两种类型，并提供了一些必要条件和充分条件存在的相合检验。我们强调，没有假设的过程分布超越平稳性和遍历性。
英文摘要：
Given a finite-valued sample $X_1,...,X_n$ we wish to test whether it was generated by a stationary ergodic process belonging to a family $H_0$, or it was generated by a stationary ergodic process outside $H_0$. We require the Type I error of the test to be uniformly bounded, while the type II error has to be mande not more than a finite number of times with probability 1. For this notion of consistency we provide necessary and sufficient conditions on the family $H_0$ for the existence of a consistent test. This criterion is illustrated with applications to testing for a membership to parametric families, generalizing some existing results. In addition, we analyze a stronger notion of consistency, which requires finite-sample guarantees on error of both types, and provide some necessary and some sufficient conditions for the existence of a consistent test. We emphasize that no assumption on the process distributions are made beyond stationarity and ergodicity.
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